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The Hungarian Approach and How It Fits the American Educational Landscape (2015)

174 points by jpelecanos 9y ago

maksimum 9y ago
> After the student investigation, the teacher highlights important ideas embedded in a concrete problem, and summarizes and generalizes their findings. In particular, the teacher’s summary makes sense and is meaningful, because students have had the experience of playing around with these ideas on their own before coming together to formalize them as a class. It's important for students to get their hands on examples and play with the ideas we're trying to present on their own. One issue I have is that this takes so much time. If you're introducing concepts that the students don't have good intuition about, you have to go so slowly. Even then it feels like some students can't follow. I think it's beneficial when it's possible to get students to engage with the material on a daily basis as reading or homework. Hard to do when they're expected to take 4 classes (college) or 6-8 (high school) and dedicate study time to each of them.
- gizmo686 9y ago
  When you use this approach, you generally cover less material, but cover it better. For most classes, this seems like a good tradeoff. 4 classes isn't really that much. You can essentially replace the time students would normally spend "studying" with them spending that time working on the problems. Further, in my experience, this type of work is far more engaging than traditional studying, so it is easier for students to spend time on it; and the time they do spend tends to be more thoughtfull.
  - jacobolus 9y ago
    Moreover, as people practice, they can get generically better at meta-skills such as (in no particular order) skimming, close reading, constructing mental outlines of arguments, drawing diagrams and pictures, inventing examples to match given specifications, testing concrete examples against abstract statements, generalizing specific relationships discovered in the examples to abstract laws and proving them generically, discarding or modifying abstractions to better match a wider collection of examples, working backwards, discarding dead-end problem-solving strategies while mining them for partial useful results, breaking problems down into manageable pieces, deductive logic, generating hypotheses likely to be interesting, abandoning whole problems which turn out to be too hard and switching to something else, cross-applying solution strategies from one field to another, simplifying complex arguments by discarding or separating extraneous or duplicated steps, writing up explanations in clear and coherent way for various audiences, researching past work in an efficient way, diving into new fields with completely alien notation and terminology and quickly taking the lay of the land, and so on. These skills are more generically useful than recipes or collections of facts about any particular subject, because they serve as multipliers for quite generic learning and problem-solving efficiency. One big problem with trying to teach a single specific course in a very problem-centered / student-driven / socratic style is that often students have not been sufficiently trained in any of these meta skills, and as a result move at much slower pace than their potential because they waste a lot of time on inefficient problem-solving methods, get side-tracked, throw away useful work, explain things poorly, don’t get around to crystallizing their useful results, and so on. The more courses get taught in this style, the faster each subsequent course can move as students figure out how to learn effectively.
    - katdev 9y ago
      That's a nice list of meta-skills. Do you have any further reading to recommend on identifying/teaching meta-skills?
      - jacobolus 9y ago
        You could try Polya’s How to Solve It, and follow up with Schoenfeld’s Mathematical Problem Solving (which cites a lot of other material). These are rather focused on problem solving per se, and don’t really discuss larger-scale strategies for research or learning. You can try just diving into child development and education literature. Not sure what out there really tries to be comprehensive in summarizing the best techniques for teaching and learning arbitrary meta-skills.
- gjulianm 9y ago
  I think this approach is better suited to lower level schooling, where kids already spend several years learning and practicing a small number of concepts. Instead of making them do countless calculations and mechanical problems, invest some of that time in abilities that will actually stick with them and be useful in the future.
niftich 9y ago
I took my first eight years of math in Hungary; admittedly, some time ago. Though I'm not sure if things have changed since then, or were different at higher levels, the way the article describes it very much reflected my experience. Starting out, there was a balanced mix of rote learning the basics (as it was done in other subjects), then moving towards creativity and gradual, independent rediscovery, and it was done so in a way that didn't feel stifling if you somehow knew to do it a different way. Ultimately it's a small country; there was a math bee you could compete in at a local level, and then your district would send the best representatives to the countrywide event. It was a prestigious event, and pretty stressful, but ultimately fun. The questions asked at the national competition were always really oddball and obscure and required both creativity and judicious use of everything you've learned. Come think of it, the culture of the competitions in various subjects made school really fun. Some other aspects of my primary school education in Hungary were not so stellar. In other subjects, there was very much a focus on facts in isolation, without really understanding or delving into context, notably in History. Literature I also found limiting, as much emphasis was placed on poetry analysis, which I found to be subjective; nonetheless, diverging from commonly accepted analyses was did not result in a good mark. When I came to the US, I found an emphasis on critical thinking in the Humanities, which was a breath of fresh air. But in math and science, the quality and method of instruction in Hungary was top-notch.
- koube 9y ago
  Why is Hungarian math so forward looking but not the other subjects? Is Hungary especially good at math?
  - underwoodley 9y ago
    It's difficult to generalize, but by pretty much any metric you choose Hungary produced a massively disproportionate share of the outstanding mathematicians of the twentieth century.
    - tehlike 9y ago
      can you give couple examples that are most prominent?
gizmo686 9y ago
I would to see this approach applied more in the sciences as well. I my college syntax (linguistics) class, most of the teaching was done by the teacher giving us a (carefully curated) set of data to explain as homework. Class time was spent making sure everyone got to the same answer and understood the arguments behind it. When there are multiple reasonable answers, they also made sure that students understand the other ones and why we rejected them (sometimes the reason is as simple as 'we need to pick an answer, lets just vote'; other times it is 'both are reasonable explanations, the field went with B, read Chomsky 1987 if you want to know why.'). We would then generally talk about problems we still have (especially if the data was English, and students could come up with new data that didn't work as nicely).
- pmoriarty 9y ago
  "Class time was spent making sure everyone got to the same answer and understood the arguments behind it." How many students were in your class? With the typical undergraduate class sizes that I've TA'ed at (about 30 students or so), there's just not enough time during the class to go over everything with each person individually and explain everything to them if they don't get it. Even if there was time, if someone is slow the rest of the class will be bored to death waiting for you to explain something to them (possibly over and over until they get it). Some of the more advanced students will be bored by any explanation, while the most detailed explanations with many examples are necessary for other students. There are office hours and lab time, and some students make the most of that, but some don't. I actually spent a lot of my time helping out students who were lagging behind and needed a lot of attention, and wound up kind of neglecting the talented ones who didn't need any help, but who I think would have gotten more out of the class if we were able to engage them more, challenge them more, and cater to their interests more rather than trying to cater to the lowest common denominator. I'm not sure what the right answer here is in classes where students vary widely in skills, interests, and abilities.
  - gizmo686 9y ago
    25. It also does not typically require much individual attention; generally presenting a cleaned up version of the arguement is enough. If multiple students have a problem, they tend to have the same problem, so the work scales sublinearly. Of course, larger class sizes will always make teaching more difficult.
jonsen 9y ago
Math is much more than what I was taught in school. I discovered that as a child when stumbling upon this Hungarian math book at the local library: https://www.amazon.com/Playing-Infinity-Dover-Books-Mathematics-ebook/dp/B00A73IWVY/ https://www.amazon.com/Playing-Infinity-Dover-Books-Mathemat...
- fogetti 9y ago
  Hey, that looks awesome! Thanks for recommending it. I put it on my bucket list.
AJRF 9y ago
I'm not "bad" at math per se, but would there be much benefit in going from the ground up learning in the Hungarian form? I guess you could blow through the first 7~10 years of schooling in less than a year of dedicated study, but teaching yourself just up to before college level would take you a few years, right? Is there any online courses that have this content?
- patkai 9y ago
  Reading George Polya's books might be a way of learning this technique. At least they explain very well the method of thinking about math.
loriverkutya 9y ago
As a hungarian, I'm pretty surprised by this article, since the quality of hungarian education is getting worse and worse, thanks to the "reforms", which basically means they are spending less and less on education on all level. And however in the past, math education was world class, now the "old school" teachers are retiring and other than a handful of elite schools (Fazekas, Eötvös, Radnóti etc) most of the schools are way below the european average. (source: https://www.compareyourcountry.org/pisa/country/hun https://www.compareyourcountry.org/pisa/country/hun ) Also usually only one or two hungarian university manage to get to any of the "best 500 universities in the world" list.
- kvch_ 9y ago
  I would not say that they are doing it on all levels on purpose. (They are just not involving people who actually know how education works.) But it is visible that they are preferring skilled workers to satisfy the requirements of EU by providing cheap workforce who can work in factories or doing other manual works. Don't misunderstand me, I deeply oppose the current education politics. I am just saying that I think I understand why they do it and why they might think that Hungary can profit from it.
- baxtr 9y ago
  > since the quality of hungarian education is getting worse and worse, thanks to the "reforms", which basically means they are spending less and less on education on all level I always wondered what good metrics are to measure the quality of education. Since you say “worse and worse” can you share any insight to that? I mean you could potentially refer to the OECD world rankings but somehow I don’t trust those lists, since they “feel” quite mechanistic.
  - kbart 9y ago
    I'm not the OP, but I'm from another Eastern Europe country where education level falls fast and dramatically. Few key indicators of that: 0. I was attending an elite gymnasium and we deliberately used old "hard science" (math, physics, chemistry) textbooks from 70'-80', because they were much more advance level than modern ones. Most of math/physics taught during first/second year at university now, was taught in 11-12th grade back then. 1. Anecdotally, but all teachers complain that every year students are getting less motivated, performing poorer, having shorter attention spans. With local "no children left behind" equivalent it's enough just to attend some percentage of classes to get passable grades. 2. Every few years some kind of "reform" is performed to reduce the difficulty of final exams to maintain failure rates at bay and keep statistics nice. 3. Combined points 1 with 2 this leads to universities full of students that have neither motivation nor skills to perform there. Since such students make up majority in most less popular programs, the difficulty level is also reduced to adapt. 4. Degrading higher level education quality reflects on its prestige as potential employees no longer trust universities to produce prospective candidates. This closes the loop back to point 1 as current pupils deem education "worthless". 5. Fun fact: entrance exams to non-prestigious universities from 70'-80' were (maybe still are) widely used as assignments in national level competitions when I was at school (late nineties to early 00'). To paraphrase that -- a skill level that once was expected from anybody who wanted to be accepted in university now puts you at the very top.
kvch_ 9y ago
For some reason I never knew that Hungarian Maths teaching is so outstanding. My high school teacher who came from Romania to Hungary always told us that he learned topics much earlier than we did. For example he learned equitations in grade 5 and we learn them in grade 7. So I figured that Romania must be better at teaching Maths. Having gone through all levels of Maths in Hungary, from elementary school until BSc of university, I want to point out that this method sounds good as long as the teacher is able to keep the attention of the class. In my school, a few teachers were unable to do that and it was a disaster. Children were playing, talking and doing nothing in classes. Even preventing others from learning the material. Fortunately, I have never had these kind of teachers. However, if someone did they were doomed at university, because the expectations were too high for them. So I think it is quite a big disadvantage in Hungary. If you miss out in high school, because you were busy being a rebellious teen, there is a good chance that you never make it. You only realize it after you started university, because it is pretty easy to get into science courses of top universities in Hungary and very hard to actually graduate.
deleted 9y ago
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leni536 9y ago
I would like to point out two of my favorite high school competitions in Hungary. One is KöMaL [1]. It's a monthly journal, one has to send back solutions to the problems. The competition is during the whole school year. It has problems from math, physics and computer science, these are separate contests. I did the "P" (theoretical physics) competition. Sometimes I took a look for the "B" math problems and I could never solve a single "A" math problem, those are freaking insane. [1] https://www.komal.hu/info/miazakomal.e.shtml https://www.komal.hu/info/miazakomal.e.shtml The second competition is the Eötvös Physics Competition [2]. Unfortunately the problems are not translated to English. This is a single round competition for the whole country. There are three physics problems fitting on a piece of A4 paper (single sided). The students can use anything (any number of books, calculator), the competition is 5 hours long. All high school and first year university students participate in the same contest. It's designed to filter out the very best physics students in the whole country (typically only one or two students can fully solve all three problems). [2] http://eik.bme.hu/~vanko/fizika/eotvos.htm http://eik.bme.hu/~vanko/fizika/eotvos.htm
- ptero 9y ago
  Russia (Soviet Union actually) had somewhat similar mail in programs that IMO we're very useful to stimulate those with high interest in specific fields beyond what a school would do. IMO stimulating and developing top end is something sorely missing in US education, which is mostly focusing on helping those behind to catch up. That is useful, but pushing 1-2% of best students as far as possible is just as important for the society long term. My 2c.
  - digi_owl 9y ago
    And mail in may be better than extra classes or similar, as it may avoid various "tall poppy" issues. And these days it can even be done electronically.
  - Viliam1234 9y ago
    Similarly in Slovakia (and Czechoslovakia historically). The highest quality education on the elementary- and high-school level happened outside the school system. So if anyone wants to reproduce this strategy, they should give up on schools completely, and create a parallel system of education. Make it fun, allow competition (with no penalties for not being good enough; you just don't get the medal), and keep it voluntary. For the remaining 99% of population... probably something like Hejny method: https://www.h-mat.cz/en/hejny-method https://www.h-mat.cz/en/hejny-method https://www.youtube.com/watch?v=xm0xsBjdMe4 https://www.youtube.com/watch?v=xm0xsBjdMe4
karllager 9y ago
A friend of mine enjoyed her first years in school in the Pannonian basin; I am not sure, whether they did something special - but it was enough to get her into a selective German high-school specialised in maths and sciences later in her life. Always admired her for the experience, as she repeatedly speak of it if it has been fun and games.
chatmasta 9y ago
My high school did something similar [0]. We never had math textbooks, only a book of problems. Each night we had 10 problems we had to solve. When we showed up in class the next day, each student would present a problem on the board and discuss their solution. It worked well for the really disciplined, rigorous kids who were super interested in math and already had a solid background in it. But for someone like me, who never quite did all the homework, it became a game of getting to class first so I could present the one problem I did last night. [0] https://en.wikipedia.org/wiki/Harkness_table https://en.wikipedia.org/wiki/Harkness_table
chx 9y ago
Let's make this very clear: this is not a typical Hungarian approach. This is what Fazekas and to an extent a few more similar specialized high schools do. The typical Hungarian approach is frontal instruction with no respect to the learning speed differences. Source: Personal experience. I am a Fazekas alumni and have a Hungarian maths teachers masters as well. I am bankrolling a very small reform school in Hungary so I am in contact with current Hungarian teachers every day and also I am obviously very interested in what's going on so I read a lot.
otakucode 9y ago
There were 2 documentaries produced by famed documentarian Frederick Wiseman called High School and High School 2. In one, a group of average students are followed through a typical high school in a middle class predominantly white area. In the second one, a group of students are followed through an experimental high school in a predominantly impoverished area with mostly a Latino population. The 'experimental' nature of the school was that every single class, every last one, was completely restructured to center around one thing: critical thinking. Teaching by fiat ('this is how it is because I say so and I am the authority') was banned. Every bit of teaching was through asking questions and having them answered, students challenging teachers on an equal intellectual playing field (unequal in specific knowledge of course, but equal in capacity to reason and challenge assumptions). The experimental school produced the highest proportion of students to go on to receive college degrees (not just attend college, but finish) every seen in the country. The results were absolutely amazing and tremendously good. But... it's harder for teachers to teach that way. They can't plan ahead. They have to know their subjects inside and out, not just read off of a lesson plan. If a student asks a question that the teacher can't answer, the teacher has to admit it and try to figure it out with them, which many teachers are not emotionally mature enough to participate in alongside an adolescent. It gives a great deal of power and agency to adolescents, and our society is obsessed with stripping adolescents of every iota of control over their own life and denigrating them as much as possible. So widespread adoption of such schooling cannot gain much support at all. The documentaries also did a good job showing how the "traditional" schooling methods broke the 'spirit' of adolescents and sucked the love of learning and figuring things out right out of them, turning them into disinterested husks of human beings, while the experimental school left them as vibrantly full of a love of life and learning as they entered it. Such things are of course difficult to measure and generally distrusted by our "pleasure is a sure sign of hidden dangers" mentality.
tioga 9y ago
I grew up and studied math in Hungary and graduated from Fazekas, the school mentioned in the atricle, and its "special math" high school class. I also spent a year in high school in the US so I have some basis for comparison. My experience was pretty much exactly as described in the article as well and I am forever grateful for the school and my teachers for giving me a foundation I could build on later in life. I'd like to point out a few things though, others have already touched upon some of these: First, similar to why it's hard to replicate the Silicon Valley startup model elsewhere (or at least why it takes such a long time), the issue is somewhat similar here. The method of teaching is just one part of the equation. It was a whole "ecosystem" of fantastically knowledgable and respected teachers who could anywhere else be university professors or researchers, publications (such as KoMaL), camps, competitions and other extracurricular activities aimed at elementary and high school students, and a culture of math and science being interesting and fun vs. the stereotypical hard and boring. The way of teaching feels a little bit more of a consequence of this culture rather than the source. You can pick your own preferred origin story for how that culture emerged: a booming industrial economy in the age of the Austro-Hungarian empire, a multi-ethnic, liberal (in the original sense of the word and given the context) country, the migration and resulting concentration of Jews in Budapest, or a series of exceptional teachers and mentors. The highly visible world-wide successes in the first half of the 20th century then later provided an on-going narrative that benefited the national ethos and hence made plenty of funding available in the second half (conveniently forgetting the austro-hungarian, the economic boom, the liberal or the jewish part of the story). But in any case the culture and the support system is (or at least was) there and that one is very hard to replicate at a broad scale, although certainly easier within specific communities. As someone mentioned, even in Hungary it is not broadly present and is limited to a certain set of top schools. Also, there is a flip side to this story. Personally, I really liked math before going to high school and completely lost interest by the time I finished. Partly because a lot of kids around me were much better so I felt like a failure, partly because I was more interested in computers and programming and also in finance, all of which was looked down upon. The prestige of winning a programming competition was nowhere near the same as placing well in math or physics. Working as a developer on the side was considered a distraction. I think this was for the better for me personally. A decent number of my classmates got burnt out and had severe depressions due to the pressure. You were almost expected to win a gold medal at the International Olympiad and eventually become a world-wide math celebrity. I can't shake the feeling that a lot of them "peaked" at the end of high school, although perhaps that's partly the result of the rapidly declining university system. Again, I'm very grateful for what I got but it's more in terms creative thinking and problem solving than specific math skills. In fact, I got to learn other subjects, such as history and literature through the same method which I now realize is very unusual in a country where those subjects are usually heavily biased toward insitilling a national identity as opposed to fostering independent thinking.

174 points by jpelecanos 9y ago

> After the student investigation, the teacher highlights important ideas embedded in a concrete problem, and summarizes and generalizes their findings. In particular, the teacher’s summary makes sense and is meaningful, because students have had the experience of playing around with these ideas on their own before coming together to formalize them as a class. It's important for students to get their hands on examples and play with the ideas we're trying to present on their own. One issue I have is that this takes so much time. If you're introducing concepts that the students don't have good intuition about, you have to go so slowly. Even then it feels like some students can't follow. I think it's beneficial when it's possible to get students to engage with the material on a daily basis as reading or homework. Hard to do when they're expected to take 4 classes (college) or 6-8 (high school) and dedicate study time to each of them.

gizmo686 9y ago
When you use this approach, you generally cover less material, but cover it better. For most classes, this seems like a good tradeoff. 4 classes isn't really that much. You can essentially replace the time students would normally spend "studying" with them spending that time working on the problems. Further, in my experience, this type of work is far more engaging than traditional studying, so it is easier for students to spend time on it; and the time they do spend tends to be more thoughtfull.
- jacobolus 9y ago
  Moreover, as people practice, they can get generically better at meta-skills such as (in no particular order) skimming, close reading, constructing mental outlines of arguments, drawing diagrams and pictures, inventing examples to match given specifications, testing concrete examples against abstract statements, generalizing specific relationships discovered in the examples to abstract laws and proving them generically, discarding or modifying abstractions to better match a wider collection of examples, working backwards, discarding dead-end problem-solving strategies while mining them for partial useful results, breaking problems down into manageable pieces, deductive logic, generating hypotheses likely to be interesting, abandoning whole problems which turn out to be too hard and switching to something else, cross-applying solution strategies from one field to another, simplifying complex arguments by discarding or separating extraneous or duplicated steps, writing up explanations in clear and coherent way for various audiences, researching past work in an efficient way, diving into new fields with completely alien notation and terminology and quickly taking the lay of the land, and so on. These skills are more generically useful than recipes or collections of facts about any particular subject, because they serve as multipliers for quite generic learning and problem-solving efficiency. One big problem with trying to teach a single specific course in a very problem-centered / student-driven / socratic style is that often students have not been sufficiently trained in any of these meta skills, and as a result move at much slower pace than their potential because they waste a lot of time on inefficient problem-solving methods, get side-tracked, throw away useful work, explain things poorly, don’t get around to crystallizing their useful results, and so on. The more courses get taught in this style, the faster each subsequent course can move as students figure out how to learn effectively.
  - katdev 9y ago
    That's a nice list of meta-skills. Do you have any further reading to recommend on identifying/teaching meta-skills?
    - jacobolus 9y ago
      You could try Polya’s How to Solve It, and follow up with Schoenfeld’s Mathematical Problem Solving (which cites a lot of other material). These are rather focused on problem solving per se, and don’t really discuss larger-scale strategies for research or learning. You can try just diving into child development and education literature. Not sure what out there really tries to be comprehensive in summarizing the best techniques for teaching and learning arbitrary meta-skills.
gjulianm 9y ago
I think this approach is better suited to lower level schooling, where kids already spend several years learning and practicing a small number of concepts. Instead of making them do countless calculations and mechanical problems, invest some of that time in abilities that will actually stick with them and be useful in the future.

niftich 9y ago

I took my first eight years of math in Hungary; admittedly, some time ago. Though I'm not sure if things have changed since then, or were different at higher levels, the way the article describes it very much reflected my experience. Starting out, there was a balanced mix of rote learning the basics (as it was done in other subjects), then moving towards creativity and gradual, independent rediscovery, and it was done so in a way that didn't feel stifling if you somehow knew to do it a different way. Ultimately it's a small country; there was a math bee you could compete in at a local level, and then your district would send the best representatives to the countrywide event. It was a prestigious event, and pretty stressful, but ultimately fun. The questions asked at the national competition were always really oddball and obscure and required both creativity and judicious use of everything you've learned. Come think of it, the culture of the competitions in various subjects made school really fun. Some other aspects of my primary school education in Hungary were not so stellar. In other subjects, there was very much a focus on facts in isolation, without really understanding or delving into context, notably in History. Literature I also found limiting, as much emphasis was placed on poetry analysis, which I found to be subjective; nonetheless, diverging from commonly accepted analyses was did not result in a good mark. When I came to the US, I found an emphasis on critical thinking in the Humanities, which was a breath of fresh air. But in math and science, the quality and method of instruction in Hungary was top-notch.

koube 9y ago
Why is Hungarian math so forward looking but not the other subjects? Is Hungary especially good at math?
- underwoodley 9y ago
  It's difficult to generalize, but by pretty much any metric you choose Hungary produced a massively disproportionate share of the outstanding mathematicians of the twentieth century.
  - tehlike 9y ago
    can you give couple examples that are most prominent?

gizmo686 9y ago

I would to see this approach applied more in the sciences as well. I my college syntax (linguistics) class, most of the teaching was done by the teacher giving us a (carefully curated) set of data to explain as homework. Class time was spent making sure everyone got to the same answer and understood the arguments behind it. When there are multiple reasonable answers, they also made sure that students understand the other ones and why we rejected them (sometimes the reason is as simple as 'we need to pick an answer, lets just vote'; other times it is 'both are reasonable explanations, the field went with B, read Chomsky 1987 if you want to know why.'). We would then generally talk about problems we still have (especially if the data was English, and students could come up with new data that didn't work as nicely).

pmoriarty 9y ago
"Class time was spent making sure everyone got to the same answer and understood the arguments behind it." How many students were in your class? With the typical undergraduate class sizes that I've TA'ed at (about 30 students or so), there's just not enough time during the class to go over everything with each person individually and explain everything to them if they don't get it. Even if there was time, if someone is slow the rest of the class will be bored to death waiting for you to explain something to them (possibly over and over until they get it). Some of the more advanced students will be bored by any explanation, while the most detailed explanations with many examples are necessary for other students. There are office hours and lab time, and some students make the most of that, but some don't. I actually spent a lot of my time helping out students who were lagging behind and needed a lot of attention, and wound up kind of neglecting the talented ones who didn't need any help, but who I think would have gotten more out of the class if we were able to engage them more, challenge them more, and cater to their interests more rather than trying to cater to the lowest common denominator. I'm not sure what the right answer here is in classes where students vary widely in skills, interests, and abilities.
- gizmo686 9y ago
  25. It also does not typically require much individual attention; generally presenting a cleaned up version of the arguement is enough. If multiple students have a problem, they tend to have the same problem, so the work scales sublinearly. Of course, larger class sizes will always make teaching more difficult.

jonsen 9y ago

Math is much more than what I was taught in school. I discovered that as a child when stumbling upon this Hungarian math book at the local library: https://www.amazon.com/Playing-Infinity-Dover-Books-Mathematics-ebook/dp/B00A73IWVY/ https://www.amazon.com/Playing-Infinity-Dover-Books-Mathemat...

fogetti 9y ago
Hey, that looks awesome! Thanks for recommending it. I put it on my bucket list.

AJRF 9y ago

I'm not "bad" at math per se, but would there be much benefit in going from the ground up learning in the Hungarian form? I guess you could blow through the first 7~10 years of schooling in less than a year of dedicated study, but teaching yourself just up to before college level would take you a few years, right? Is there any online courses that have this content?

patkai 9y ago
Reading George Polya's books might be a way of learning this technique. At least they explain very well the method of thinking about math.

loriverkutya 9y ago

As a hungarian, I'm pretty surprised by this article, since the quality of hungarian education is getting worse and worse, thanks to the "reforms", which basically means they are spending less and less on education on all level. And however in the past, math education was world class, now the "old school" teachers are retiring and other than a handful of elite schools (Fazekas, Eötvös, Radnóti etc) most of the schools are way below the european average. (source: https://www.compareyourcountry.org/pisa/country/hun https://www.compareyourcountry.org/pisa/country/hun ) Also usually only one or two hungarian university manage to get to any of the "best 500 universities in the world" list.

kvch_ 9y ago
I would not say that they are doing it on all levels on purpose. (They are just not involving people who actually know how education works.) But it is visible that they are preferring skilled workers to satisfy the requirements of EU by providing cheap workforce who can work in factories or doing other manual works. Don't misunderstand me, I deeply oppose the current education politics. I am just saying that I think I understand why they do it and why they might think that Hungary can profit from it.
baxtr 9y ago
> since the quality of hungarian education is getting worse and worse, thanks to the "reforms", which basically means they are spending less and less on education on all level I always wondered what good metrics are to measure the quality of education. Since you say “worse and worse” can you share any insight to that? I mean you could potentially refer to the OECD world rankings but somehow I don’t trust those lists, since they “feel” quite mechanistic.
- kbart 9y ago
  I'm not the OP, but I'm from another Eastern Europe country where education level falls fast and dramatically. Few key indicators of that: 0. I was attending an elite gymnasium and we deliberately used old "hard science" (math, physics, chemistry) textbooks from 70'-80', because they were much more advance level than modern ones. Most of math/physics taught during first/second year at university now, was taught in 11-12th grade back then. 1. Anecdotally, but all teachers complain that every year students are getting less motivated, performing poorer, having shorter attention spans. With local "no children left behind" equivalent it's enough just to attend some percentage of classes to get passable grades. 2. Every few years some kind of "reform" is performed to reduce the difficulty of final exams to maintain failure rates at bay and keep statistics nice. 3. Combined points 1 with 2 this leads to universities full of students that have neither motivation nor skills to perform there. Since such students make up majority in most less popular programs, the difficulty level is also reduced to adapt. 4. Degrading higher level education quality reflects on its prestige as potential employees no longer trust universities to produce prospective candidates. This closes the loop back to point 1 as current pupils deem education "worthless". 5. Fun fact: entrance exams to non-prestigious universities from 70'-80' were (maybe still are) widely used as assignments in national level competitions when I was at school (late nineties to early 00'). To paraphrase that -- a skill level that once was expected from anybody who wanted to be accepted in university now puts you at the very top.

kvch_ 9y ago

For some reason I never knew that Hungarian Maths teaching is so outstanding. My high school teacher who came from Romania to Hungary always told us that he learned topics much earlier than we did. For example he learned equitations in grade 5 and we learn them in grade 7. So I figured that Romania must be better at teaching Maths. Having gone through all levels of Maths in Hungary, from elementary school until BSc of university, I want to point out that this method sounds good as long as the teacher is able to keep the attention of the class. In my school, a few teachers were unable to do that and it was a disaster. Children were playing, talking and doing nothing in classes. Even preventing others from learning the material. Fortunately, I have never had these kind of teachers. However, if someone did they were doomed at university, because the expectations were too high for them. So I think it is quite a big disadvantage in Hungary. If you miss out in high school, because you were busy being a rebellious teen, there is a good chance that you never make it. You only realize it after you started university, because it is pretty easy to get into science courses of top universities in Hungary and very hard to actually graduate.

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leni536 9y ago

I would like to point out two of my favorite high school competitions in Hungary. One is KöMaL [1]. It's a monthly journal, one has to send back solutions to the problems. The competition is during the whole school year. It has problems from math, physics and computer science, these are separate contests. I did the "P" (theoretical physics) competition. Sometimes I took a look for the "B" math problems and I could never solve a single "A" math problem, those are freaking insane. [1] https://www.komal.hu/info/miazakomal.e.shtml https://www.komal.hu/info/miazakomal.e.shtml The second competition is the Eötvös Physics Competition [2]. Unfortunately the problems are not translated to English. This is a single round competition for the whole country. There are three physics problems fitting on a piece of A4 paper (single sided). The students can use anything (any number of books, calculator), the competition is 5 hours long. All high school and first year university students participate in the same contest. It's designed to filter out the very best physics students in the whole country (typically only one or two students can fully solve all three problems). [2] http://eik.bme.hu/~vanko/fizika/eotvos.htm http://eik.bme.hu/~vanko/fizika/eotvos.htm

ptero 9y ago
Russia (Soviet Union actually) had somewhat similar mail in programs that IMO we're very useful to stimulate those with high interest in specific fields beyond what a school would do. IMO stimulating and developing top end is something sorely missing in US education, which is mostly focusing on helping those behind to catch up. That is useful, but pushing 1-2% of best students as far as possible is just as important for the society long term. My 2c.
- digi_owl 9y ago
  And mail in may be better than extra classes or similar, as it may avoid various "tall poppy" issues. And these days it can even be done electronically.
- Viliam1234 9y ago
  Similarly in Slovakia (and Czechoslovakia historically). The highest quality education on the elementary- and high-school level happened outside the school system. So if anyone wants to reproduce this strategy, they should give up on schools completely, and create a parallel system of education. Make it fun, allow competition (with no penalties for not being good enough; you just don't get the medal), and keep it voluntary. For the remaining 99% of population... probably something like Hejny method: https://www.h-mat.cz/en/hejny-method https://www.h-mat.cz/en/hejny-method https://www.youtube.com/watch?v=xm0xsBjdMe4 https://www.youtube.com/watch?v=xm0xsBjdMe4

karllager 9y ago

A friend of mine enjoyed her first years in school in the Pannonian basin; I am not sure, whether they did something special - but it was enough to get her into a selective German high-school specialised in maths and sciences later in her life. Always admired her for the experience, as she repeatedly speak of it if it has been fun and games.

chatmasta 9y ago

My high school did something similar [0]. We never had math textbooks, only a book of problems. Each night we had 10 problems we had to solve. When we showed up in class the next day, each student would present a problem on the board and discuss their solution. It worked well for the really disciplined, rigorous kids who were super interested in math and already had a solid background in it. But for someone like me, who never quite did all the homework, it became a game of getting to class first so I could present the one problem I did last night. [0] https://en.wikipedia.org/wiki/Harkness_table https://en.wikipedia.org/wiki/Harkness_table

chx 9y ago

Let's make this very clear: this is not a typical Hungarian approach. This is what Fazekas and to an extent a few more similar specialized high schools do. The typical Hungarian approach is frontal instruction with no respect to the learning speed differences. Source: Personal experience. I am a Fazekas alumni and have a Hungarian maths teachers masters as well. I am bankrolling a very small reform school in Hungary so I am in contact with current Hungarian teachers every day and also I am obviously very interested in what's going on so I read a lot.

otakucode 9y ago

There were 2 documentaries produced by famed documentarian Frederick Wiseman called High School and High School 2. In one, a group of average students are followed through a typical high school in a middle class predominantly white area. In the second one, a group of students are followed through an experimental high school in a predominantly impoverished area with mostly a Latino population. The 'experimental' nature of the school was that every single class, every last one, was completely restructured to center around one thing: critical thinking. Teaching by fiat ('this is how it is because I say so and I am the authority') was banned. Every bit of teaching was through asking questions and having them answered, students challenging teachers on an equal intellectual playing field (unequal in specific knowledge of course, but equal in capacity to reason and challenge assumptions). The experimental school produced the highest proportion of students to go on to receive college degrees (not just attend college, but finish) every seen in the country. The results were absolutely amazing and tremendously good. But... it's harder for teachers to teach that way. They can't plan ahead. They have to know their subjects inside and out, not just read off of a lesson plan. If a student asks a question that the teacher can't answer, the teacher has to admit it and try to figure it out with them, which many teachers are not emotionally mature enough to participate in alongside an adolescent. It gives a great deal of power and agency to adolescents, and our society is obsessed with stripping adolescents of every iota of control over their own life and denigrating them as much as possible. So widespread adoption of such schooling cannot gain much support at all. The documentaries also did a good job showing how the "traditional" schooling methods broke the 'spirit' of adolescents and sucked the love of learning and figuring things out right out of them, turning them into disinterested husks of human beings, while the experimental school left them as vibrantly full of a love of life and learning as they entered it. Such things are of course difficult to measure and generally distrusted by our "pleasure is a sure sign of hidden dangers" mentality.

tioga 9y ago

I grew up and studied math in Hungary and graduated from Fazekas, the school mentioned in the atricle, and its "special math" high school class. I also spent a year in high school in the US so I have some basis for comparison. My experience was pretty much exactly as described in the article as well and I am forever grateful for the school and my teachers for giving me a foundation I could build on later in life. I'd like to point out a few things though, others have already touched upon some of these: First, similar to why it's hard to replicate the Silicon Valley startup model elsewhere (or at least why it takes such a long time), the issue is somewhat similar here. The method of teaching is just one part of the equation. It was a whole "ecosystem" of fantastically knowledgable and respected teachers who could anywhere else be university professors or researchers, publications (such as KoMaL), camps, competitions and other extracurricular activities aimed at elementary and high school students, and a culture of math and science being interesting and fun vs. the stereotypical hard and boring. The way of teaching feels a little bit more of a consequence of this culture rather than the source. You can pick your own preferred origin story for how that culture emerged: a booming industrial economy in the age of the Austro-Hungarian empire, a multi-ethnic, liberal (in the original sense of the word and given the context) country, the migration and resulting concentration of Jews in Budapest, or a series of exceptional teachers and mentors. The highly visible world-wide successes in the first half of the 20th century then later provided an on-going narrative that benefited the national ethos and hence made plenty of funding available in the second half (conveniently forgetting the austro-hungarian, the economic boom, the liberal or the jewish part of the story). But in any case the culture and the support system is (or at least was) there and that one is very hard to replicate at a broad scale, although certainly easier within specific communities. As someone mentioned, even in Hungary it is not broadly present and is limited to a certain set of top schools. Also, there is a flip side to this story. Personally, I really liked math before going to high school and completely lost interest by the time I finished. Partly because a lot of kids around me were much better so I felt like a failure, partly because I was more interested in computers and programming and also in finance, all of which was looked down upon. The prestige of winning a programming competition was nowhere near the same as placing well in math or physics. Working as a developer on the side was considered a distraction. I think this was for the better for me personally. A decent number of my classmates got burnt out and had severe depressions due to the pressure. You were almost expected to win a gold medal at the International Olympiad and eventually become a world-wide math celebrity. I can't shake the feeling that a lot of them "peaked" at the end of high school, although perhaps that's partly the result of the rapidly declining university system. Again, I'm very grateful for what I got but it's more in terms creative thinking and problem solving than specific math skills. In fact, I got to learn other subjects, such as history and literature through the same method which I now realize is very unusual in a country where those subjects are usually heavily biased toward insitilling a national identity as opposed to fostering independent thinking.